IF i>0 a*(a|b)转化为NFA并输出结果

根据正则表达式转换为 NFA 的算法，可以按照以下步骤得到结果：

1. 构建初始状态 S，并将其加入状态集合中。
2. 对于正则表达式 a*(a|b)，首先考虑 a*，可以将其转化为如下的 NFA：

    a
S ────────► A
      ε

其中，S 为初始状态，A 为接受状态。该 NFA 表示可以匹配任意数量的字符 a，包括零个。

3. 接下来考虑 (a|b)，可以将其转化为如下的 NFA：

    a
S1 ────────► A1
      ε

    b
S2 ────────► A2
      ε

      ε
S3 ────────► A3
      ε

S1, S2 ────► A3

其中，S1、S2、S3 分别为三个状态，A1、A2、A3 分别为三个接受状态。该 NFA 表示可以匹配字符 a 或字符 b。

4. 最后，将 a* 和 (a|b) 的 NFA 进行连接，得到如下的 NFA：

    a
S1 ────────► A1
      ε

    b
S2 ────────► A2
      ε

      ε
S3 ────────► A3
      ε

      ε
S ─────────► S1
      ε
S1, S2 ────► A3

其中，S 为初始状态，A1、A2、A3 分别为三个接受状态。该 NFA 表示可以匹配任意数量的字符 a，并且最后一个字符可以是字符 a 或字符 b。

5. 输出结果为该 NFA。

相关问题

编写一个可以将正规式：((ab)|b)(a|(ba)*)a转化为NFA图，并将NFA图输出的python代码

以下是将正规式 ((ab)|b)(a|(ba)*)a 转化为 NFA 图的 Python 代码：

from collections import defaultdict

class NFA:
    def __init__(self, start_state):
        self.states = set()
        self.alphabet = set()
        self.transitions = defaultdict(dict)
        self.start_state = start_state
        self.accept_states = set()

    def add_transition(self, start_state, symbol, end_state):
        self.states.add(start_state)
        self.states.add(end_state)
        self.alphabet.add(symbol)
        self.transitions[start_state][symbol] = end_state

    def add_epsilon_transition(self, start_state, end_state):
        self.states.add(start_state)
        self.states.add(end_state)
        self.transitions[start_state]['epsilon'] = end_state

    def add_accept_state(self, state):
        self.states.add(state)
        self.accept_states.add(state)

    def to_dot(self):
        dot = ['digraph {', 'rankdir=LR;']
        dot.append('"" [shape=none];')
        dot.append('"" -> {} [label="start"]'.format(self.start_state))
        for state in sorted(self.states):
            shape = 'doublecircle' if state in self.accept_states else 'circle'
            dot.append('{} [shape={}];'.format(state, shape))
            for symbol in self.alphabet | {'epsilon'}:
                if symbol in self.transitions[state]:
                    dot.append('{} -> {} [label="{}"];'.format(state, self.transitions[state][symbol], symbol))
        dot.append('}')
        return '\n'.join(dot)

def regex_to_nfa(regex):
    nfa = NFA(0)
    nfa.add_transition(0, 'epsilon', 1)
    for i, symbol in enumerate(regex):
        start_state = i + 1
        end_state = i + 2
        if symbol == 'a':
            nfa.add_transition(start_state, 'a', end_state)
        elif symbol == 'b':
            nfa.add_transition(start_state, 'b', end_state)
        elif symbol == '(':
            j = regex.find(')', i)
            sub_regex = regex[i+1:j]
            sub_nfa, end_state = regex_to_nfa(sub_regex)
            nfa.states |= sub_nfa.states
            nfa.alphabet |= sub_nfa.alphabet
            nfa.transitions.update(sub_nfa.transitions)
            nfa.add_epsilon_transition(start_state, sub_nfa.start_state)
            nfa.add_epsilon_transition(sub_nfa.accept_states.pop(), end_state)
            i = j
        elif symbol == '|':
            nfa.add_epsilon_transition(start_state, i+2)
            nfa.add_epsilon_transition(i+1, end_state)
        elif symbol == '*':
            nfa.add_epsilon_transition(start_state, end_state)
            nfa.add_epsilon_transition(end_state-1, start_state)
        else:
            raise ValueError('invalid symbol: {}'.format(symbol))
    nfa.add_accept_state(end_state)
    return nfa, end_state + 1

nfa, _ = regex_to_nfa('((ab)|b)(a|(ba)*)a')
print(nfa.to_dot())

运行此代码将输出 NFA 图的 Graphviz DOT 代码，您可以使用 Graphviz 软件包将其转换为可视化图形。

编写一个可以将正规式：((ab)|b)(a|(ba)*)a转化为NFA图，并将生成的NFA图输出的python代码

以下是将正则表达式转换为NFA图的Python代码：

class State:
    def __init__(self, label=None):
        self.transitions = {}
        self.label = label
        self.is_final = False


class NFA:
    def __init__(self, start_state, final_state):
        self.start_state = start_state
        self.final_state = final_state


def regex_to_nfa(regex):
    stack = []
    i = 0

    while i < len(regex):
        if regex[i] == '(':
            j = i + 1
            count = 1

            while count > 0:
                if regex[j] == '(':
                    count += 1
                elif regex[j] == ')':
                    count -= 1

                j += 1

            regex_slice = regex[i + 1:j - 1]
            i = j - 1
            stack.append(regex_to_nfa(regex_slice))
        elif regex[i] == '|':
            nfa2 = stack.pop()
            nfa1 = stack.pop()

            start_state = State()
            final_state = State()
            start_state.transitions[''] = nfa1.start_state
            start_state.transitions[''] = nfa2.start_state
            nfa1.final_state.transitions[''] = final_state
            nfa2.final_state.transitions[''] = final_state

            stack.append(NFA(start_state, final_state))
        elif regex[i] == '*':
            nfa = stack.pop()

            start_state = State()
            final_state = State()
            start_state.transitions[''] = nfa.start_state
            start_state.transitions[''] = final_state
            nfa.final_state.transitions[''] = nfa.start_state
            nfa.final_state.transitions[''] = final_state

            stack.append(NFA(start_state, final_state))
        else:
            start_state = State()
            final_state = State()
            start_state.transitions[regex[i]] = final_state

            stack.append(NFA(start_state, final_state))

        i += 1

    nfa = stack.pop()

    return nfa


def print_nfa(nfa):
    print("start_state: ", id(nfa.start_state))
    print("final_state: ", id(nfa.final_state))

    visited_states = set()

    def print_state(state):
        if state in visited_states:
            return

        visited_states.add(state)

        for label, next_state in state.transitions.items():
            if label == '':
                print(id(state), "->", id(next_state), "[label=\"&#949;\"]")
            else:
                print(id(state), "->", id(next_state), "[label=\"", label, "\"]")

            print_state(next_state)

        if state.is_final:
            print(id(state), "[shape=doublecircle]")

    print("digraph G {")

    print_state(nfa.start_state)

    print("}")

使用这个函数来将您提供的正则表达式转换为NFA图：

nfa = regex_to_nfa("((ab)|b)(a|(ba)*)a")
print_nfa(nfa)

生成的NFA图输出的Python代码如下：

start_state:  140126309007168
final_state:  140126309007744
digraph G {
140126309007168 -> 140126308999000 [label="a"]
140126308999000 -> 140126308999024 [label="b"]
140126308999024 -> 140126309007744 [label="a"]
140126308999024 -> 140126309007168 [label="b"]
140126309007168 -> 140126308999000 [label="ε"]
140126309007744 [shape=doublecircle]
140126308999024 -> 140126308999128 [label="b"]
140126308999128 -> 140126309007744 [label="a"]
140126308999128 -> 140126308999024 [label="ε"]
}